b) How many solutions are there to x1+2+x3+T4 =20 where r4 > 10 and each x; is a natural number (0 counts as a natural number for us).

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.1: Postulates For The Integers (optional)
Problem 28E
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(b) How many solutions are there to x1+x2+x3+x4= 20 where x4 > 10
and each x; is a natural number (0 counts as a natural number for
us).
(c) Let X {1,2, 3, 4, 5}. How many relations are there on X with the
property that for all x E X, x is not related to itself?
(d) Give the equivalence relation on {a, b, c, d, e} whose equivalence classes
give the partition P = {{a,b}, {c, d}, {e}}.
(e) You are dividing 112 apples among 5 boxes. What is the smallest
number of apples that could appear in the box with the most apples?
Transcribed Image Text:(b) How many solutions are there to x1+x2+x3+x4= 20 where x4 > 10 and each x; is a natural number (0 counts as a natural number for us). (c) Let X {1,2, 3, 4, 5}. How many relations are there on X with the property that for all x E X, x is not related to itself? (d) Give the equivalence relation on {a, b, c, d, e} whose equivalence classes give the partition P = {{a,b}, {c, d}, {e}}. (e) You are dividing 112 apples among 5 boxes. What is the smallest number of apples that could appear in the box with the most apples?
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